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What the author glosses over somewhat is the method of sampling. If you read the first 20 pages, find no typos, and use this rule to arrive at 15%, that could b

by madrox 8y ago

What the author glosses over somewhat is the method of sampling. If you read the first 20 pages, find no typos, and use this rule to arrive at 15%, that could be way off. He's assuming the risk of typos are evenly distributed when there's a lot of reasons it may not be. For example, the first half of the book could've been more heavily proof-read than the latter half. It's not out of the question that editors get lazier the farther they get into the book. If you were to randomly read 20 pages in a book and find no typos, 15% probability makes more sense. It's understandable to not mention this in a short blog post about the rule of three, but never forget that when you're interpreting statistics...how you build your sample matters.

bluGill 8y ago
In the case of a book the first pages are likely to be significantly better than the rest. An editor knows that once you have invested in reading the first part of the book you are unlikely to put the book down. This means the first pages have to suck you in, and not do anything to make want to quit reading. The most important part is the first sentence as this is often the only part that drives your buy/leave in the store decision.
- whatshisface 8y ago
  >The most important part is the first sentence as this is often the only part that drives your buy/leave in the store decision. I usually sample books from the middle. I wonder what the heatmap of bookstore reading really looks like?
  - bluGill 8y ago
    My informal sampling suggests most people start at first page. They worry that reading the middle or end would reveal a spoiler. It would be interesting to get good data though.
yummybear 8y ago
In the same vein if the weather is good today, there is s large probability that it’s good tomorrow, but if it’s been good for 14 days there is an increasing probability of bad weather.
- darkerside 8y ago
  Or you're more likely to be in an area with a pleasant climate
- joefourier 8y ago
  If the process is truly random however, then that no longer holds and you risk falling prey to the gambler's fallacy. If you flip a coin and get heads 14 times, you're still equally likely to get heads or tails the 15th time, despite the probability of getting heads 15 times in a row being very low.
- chowchowchow 8y ago
  Why would this be true? What if we, by luck, had 14 days of good weather at the end of monsoon season? Your observation seems to be a function of the probabilities changing as the calendar date advances and not a historical run of good weather in the past.
  - nkurz 8y ago
    Why would this be true? It's not impossible, just location dependent. In some places, there actually is a clear cycle, where the weather alternates between good and bad on a weekly cycle. The Bay Area of California, where HN is headquartered, seems to be one of those places: The Fog Cycle Week by week from spring into August, the forces that produce the fog increase in intensity. The Paciﬁc High moves farther north, closer to the latitude of San Francisco, sending out stronger winds; offshore the up-welling of cold bottom waters increases, condensing the winds’ moisture into thicker masses of fog; in the Central Valley, the northward-moving sun sends temperatures to the 100 degree mark and beyond. The hot air rises, sucking cool masses in great drafts through the only break in the Valley’s surrounding mountains, San Francisco Bay. With the ocean air comes the fog, evaporating gradually in the hot, dry air of the Valley, but sometimes penetrating at night as far as Sacramento and Stockton. The fog seems to come and go in cycles. Until recent years, the conventional explanation for the fog’s behavior was a simple one: as the cool, fog-bearing ocean air is pulled over the coastal hills and across the Bay toward the hot Central Valley (that is, from a high-pressure to a low-pressure area), the nearest parts of the Valley begin to cool off after a few days, much as a draft from an open door lowers the temperature in a warm room. The incoming cool, heavy sea air replaces the warm, rising land air, and temperatures in Sacramento and Stockton may drop from well above 100 degrees to the “cool” 90s. When the Valley cools sufficiently, the fog-producing machinery breaks down. Without the intense Valley heat to draw the sea air in through the Bay Region, the wind diminishes and no longer carries the fog inland. San Francisco, the Golden Gate, and the coastline are fog free. Then the process starts all over again. Without the incoming wind and fog, the sun gradually reheats the Valley. The rising warm air again begins to attract the foggy marine air inland. The result is a fog cycle of about a week in length, producing roughly three or four days of fog over the Bay and three or four days of sun. https://baynature.org/article/cutting-through-the-fog/ https://baynature.org/article/cutting-through-the-fog/
robluxus 8y ago
Could we apply the rule of three for the larger context here? Something along the lines of: "if I haven't seen a book with unequal typos distribution yet, what are the odds this current one will be an instance where editors got lazier in the second half?"
- madrox 8y ago
  You could, though that wouldn't be a very powerful test. You could probably construct a more powerful test if you're going through the trouble of reading that many books.
nitwit005 8y ago
Doesn't the book example need to factor in the book length? If you read 20 pages, and it's 20 pages long, you should be 100% confident, but if you read 20 pages and it's 5000 pages long, your confidence should be near 0.
- madrox 8y ago
  Not in this case, because the probably being estimated is "the chance a single page could contain a typo" and not "the chance the rest of the book could contain a typo." To do the latter, you'd need to know the length of the book, yes.
- c3534l 8y ago
  Logically not, since your sampling method is imperfect and will not detect all typos and, in fact, some typos might make perfect sense given the context and be inherently undetectable forever.
- ezzaf 8y ago
  In effect it does. If you have read 20 pages and found no typos you estimate the chance of an unknown page having a typo is 1 in 20/3. But if there is 0 unread pages then there 0 cases to apply the probability to. Make it 100 pages, then you have 100 cases each with a 1 in 20/3 probability. Of course if you read 30 more and still don't find a typo, it's now 50 remaining cases each with a 1 in 50/3 (estimated) probability.
dahart 8y ago
> It's understandable to not mention this I feel like the very first word, "Estimating" made what you're talking about pretty clear. It's extremely common for estimates to make simplifying assumptions that don't necessarily hold if you care about accuracy or specific situations. He also called the rule of three "quick and dirty". > If you were to randomly read 20 pages in a book and find no typos, 15% probability makes more sense. OTOH, if typos are actually uniformly distributed, then reading the first 20 is better than a random 20 unless you take care to pick random pages without repeats.
- mark-r 8y ago
  Interesting that you would worry about repeats. Most people would interpret "randomly read 20 pages" as "choose 20 from n" not "take 20 rand(n)".
  - dahart 8y ago
    You're right, and mathematicians and computer scientists aren't most people. We are being pedantic / precise here. If someone wants to caution that people need to be really careful about estimates because there are some assumptions involved, then it's fair to hold them to their own standard, isn't it? If typos are uniform, then the suggestion to read random pages doesn't help. And whether or not people interpret it one way most of the time, if you interpret "random" like a programmer, you've introduced a small amount of bias, right?
    - mark-r 8y ago
      As a programmer it still never would have occurred to me to interpret it that way, but maybe I'm not typical. If your random library doesn't have a choose function, it's easy enough to just shuffle a list and take the first 20.

by madrox 8y ago

bluGill 8y ago

In the case of a book the first pages are likely to be significantly better than the rest. An editor knows that once you have invested in reading the first part of the book you are unlikely to put the book down. This means the first pages have to suck you in, and not do anything to make want to quit reading. The most important part is the first sentence as this is often the only part that drives your buy/leave in the store decision.

whatshisface 8y ago
>The most important part is the first sentence as this is often the only part that drives your buy/leave in the store decision. I usually sample books from the middle. I wonder what the heatmap of bookstore reading really looks like?
- bluGill 8y ago
  My informal sampling suggests most people start at first page. They worry that reading the middle or end would reveal a spoiler. It would be interesting to get good data though.

yummybear 8y ago

In the same vein if the weather is good today, there is s large probability that it’s good tomorrow, but if it’s been good for 14 days there is an increasing probability of bad weather.

darkerside 8y ago
Or you're more likely to be in an area with a pleasant climate
joefourier 8y ago
If the process is truly random however, then that no longer holds and you risk falling prey to the gambler's fallacy. If you flip a coin and get heads 14 times, you're still equally likely to get heads or tails the 15th time, despite the probability of getting heads 15 times in a row being very low.
chowchowchow 8y ago
Why would this be true? What if we, by luck, had 14 days of good weather at the end of monsoon season? Your observation seems to be a function of the probabilities changing as the calendar date advances and not a historical run of good weather in the past.
- nkurz 8y ago
  Why would this be true? It's not impossible, just location dependent. In some places, there actually is a clear cycle, where the weather alternates between good and bad on a weekly cycle. The Bay Area of California, where HN is headquartered, seems to be one of those places: The Fog Cycle Week by week from spring into August, the forces that produce the fog increase in intensity. The Paciﬁc High moves farther north, closer to the latitude of San Francisco, sending out stronger winds; offshore the up-welling of cold bottom waters increases, condensing the winds’ moisture into thicker masses of fog; in the Central Valley, the northward-moving sun sends temperatures to the 100 degree mark and beyond. The hot air rises, sucking cool masses in great drafts through the only break in the Valley’s surrounding mountains, San Francisco Bay. With the ocean air comes the fog, evaporating gradually in the hot, dry air of the Valley, but sometimes penetrating at night as far as Sacramento and Stockton. The fog seems to come and go in cycles. Until recent years, the conventional explanation for the fog’s behavior was a simple one: as the cool, fog-bearing ocean air is pulled over the coastal hills and across the Bay toward the hot Central Valley (that is, from a high-pressure to a low-pressure area), the nearest parts of the Valley begin to cool off after a few days, much as a draft from an open door lowers the temperature in a warm room. The incoming cool, heavy sea air replaces the warm, rising land air, and temperatures in Sacramento and Stockton may drop from well above 100 degrees to the “cool” 90s. When the Valley cools sufficiently, the fog-producing machinery breaks down. Without the intense Valley heat to draw the sea air in through the Bay Region, the wind diminishes and no longer carries the fog inland. San Francisco, the Golden Gate, and the coastline are fog free. Then the process starts all over again. Without the incoming wind and fog, the sun gradually reheats the Valley. The rising warm air again begins to attract the foggy marine air inland. The result is a fog cycle of about a week in length, producing roughly three or four days of fog over the Bay and three or four days of sun. https://baynature.org/article/cutting-through-the-fog/ https://baynature.org/article/cutting-through-the-fog/

robluxus 8y ago

Could we apply the rule of three for the larger context here? Something along the lines of: "if I haven't seen a book with unequal typos distribution yet, what are the odds this current one will be an instance where editors got lazier in the second half?"

madrox 8y ago
You could, though that wouldn't be a very powerful test. You could probably construct a more powerful test if you're going through the trouble of reading that many books.

nitwit005 8y ago

Doesn't the book example need to factor in the book length? If you read 20 pages, and it's 20 pages long, you should be 100% confident, but if you read 20 pages and it's 5000 pages long, your confidence should be near 0.

madrox 8y ago
Not in this case, because the probably being estimated is "the chance a single page could contain a typo" and not "the chance the rest of the book could contain a typo." To do the latter, you'd need to know the length of the book, yes.
c3534l 8y ago
Logically not, since your sampling method is imperfect and will not detect all typos and, in fact, some typos might make perfect sense given the context and be inherently undetectable forever.
ezzaf 8y ago
In effect it does. If you have read 20 pages and found no typos you estimate the chance of an unknown page having a typo is 1 in 20/3. But if there is 0 unread pages then there 0 cases to apply the probability to. Make it 100 pages, then you have 100 cases each with a 1 in 20/3 probability. Of course if you read 30 more and still don't find a typo, it's now 50 remaining cases each with a 1 in 50/3 (estimated) probability.

dahart 8y ago

> It's understandable to not mention this I feel like the very first word, "Estimating" made what you're talking about pretty clear. It's extremely common for estimates to make simplifying assumptions that don't necessarily hold if you care about accuracy or specific situations. He also called the rule of three "quick and dirty". > If you were to randomly read 20 pages in a book and find no typos, 15% probability makes more sense. OTOH, if typos are actually uniformly distributed, then reading the first 20 is better than a random 20 unless you take care to pick random pages without repeats.

mark-r 8y ago
Interesting that you would worry about repeats. Most people would interpret "randomly read 20 pages" as "choose 20 from n" not "take 20 rand(n)".
- dahart 8y ago
  You're right, and mathematicians and computer scientists aren't most people. We are being pedantic / precise here. If someone wants to caution that people need to be really careful about estimates because there are some assumptions involved, then it's fair to hold them to their own standard, isn't it? If typos are uniform, then the suggestion to read random pages doesn't help. And whether or not people interpret it one way most of the time, if you interpret "random" like a programmer, you've introduced a small amount of bias, right?
  - mark-r 8y ago
    As a programmer it still never would have occurred to me to interpret it that way, but maybe I'm not typical. If your random library doesn't have a choose function, it's easy enough to just shuffle a list and take the first 20.